Answer :
Sure ! Here's one way to look at it that nobody ever tells you:
Remember:
-- A fraction with the same thing on the top and bottom is equal to ' 1 '.
-- You can multiply a quantity by ' 1 ' all day long without changing its value.
In order to convert units, you multiply the original quantity by one or more fractions. Each fraction has the same thing on top and bottom, but in different units, so it's equal to ' 1 '. Then you go through the expression that you've built, and 'cancel' things ... dividing a unit out where it appears on both the top and bottom.
Example:
How many seconds are there in 1 day ?
(Convert one day to units of seconds.)
(1 day) x (24 hr/day) x (60min/hr) x (60 sec/min)
That's 1 day, multiplied by 3 fractions. Each fraction is equal to ' 1 ' because it has the same thing on top and bottom, only in different units.
Now, look at the first 2 terms. They have 'day' on top and 'day' on the bottom, so 'day' can be 'canceled' (actually divided) out of the top and bottom.
Similarly, the 2nd and 3rd terms have 'hour' on top and bottom, so 'hour' can be canceled and disappear from the whole expression. The 3rd and 4th terms have 'minute' on the top and bottom, so 'minute' can be canceled.
Finally, the only unit that's still there and hasn't been cancelled is 'second'. The whole expression now says
(1) x (24) x (60) x (60 seconds) = 86,400 seconds
and there's the conversion of units from 'day' to 'second'.
The whole trick is to pick the right fractions, and to decide whether to write each fraction either right-side-up or upside-down. The idea is to decide which unit you want to get rid of, and then arrange things so that it's on top once and on the bottom once, so that you can cancel it and make it disappear.
And that's what I can give you on the topic of converting units. To me, it's always been very helpful.
Remember:
-- A fraction with the same thing on the top and bottom is equal to ' 1 '.
-- You can multiply a quantity by ' 1 ' all day long without changing its value.
In order to convert units, you multiply the original quantity by one or more fractions. Each fraction has the same thing on top and bottom, but in different units, so it's equal to ' 1 '. Then you go through the expression that you've built, and 'cancel' things ... dividing a unit out where it appears on both the top and bottom.
Example:
How many seconds are there in 1 day ?
(Convert one day to units of seconds.)
(1 day) x (24 hr/day) x (60min/hr) x (60 sec/min)
That's 1 day, multiplied by 3 fractions. Each fraction is equal to ' 1 ' because it has the same thing on top and bottom, only in different units.
Now, look at the first 2 terms. They have 'day' on top and 'day' on the bottom, so 'day' can be 'canceled' (actually divided) out of the top and bottom.
Similarly, the 2nd and 3rd terms have 'hour' on top and bottom, so 'hour' can be canceled and disappear from the whole expression. The 3rd and 4th terms have 'minute' on the top and bottom, so 'minute' can be canceled.
Finally, the only unit that's still there and hasn't been cancelled is 'second'. The whole expression now says
(1) x (24) x (60) x (60 seconds) = 86,400 seconds
and there's the conversion of units from 'day' to 'second'.
The whole trick is to pick the right fractions, and to decide whether to write each fraction either right-side-up or upside-down. The idea is to decide which unit you want to get rid of, and then arrange things so that it's on top once and on the bottom once, so that you can cancel it and make it disappear.
And that's what I can give you on the topic of converting units. To me, it's always been very helpful.
